I’ve been playing Sid Sackson’s seminal classic Can’t Stop the last few days, in its new iPad form. Although I’d (shamefully) never played it until now, simply hearing it described was enough for it to serve as partial inspiration for my own Picnic Blitz, as some reviewers have noticed.

Although I found the AI a challenge for my first few attempts, I learned quickly and, as is often the case with board game AIs, was soon able to defeat it a large majority of the time in one-on-one games. Its biggest weakness, I’ve observed, is that it does not to give enough (or perhaps any, it is hard to tell) consideration to the likelihood that you will be able to win on your next move. It will make an otherwise-sensible preparatory move to improve its odds of completing a column on its next move, without realizing that it isn’t likely to get a next move, and should instead shoot for a win immediately, even if the odds of success are small.

The choice between attempting to win on one’s current move or instead building up power to try to win on a subsequent move is a common dilemma in games; it’s embodied in a very pure form in Can’t Stop (and other press-your-luck dice games such as Nada), but it occurs frequently in other games in a more complex, harder-to-quantify way; deciding when to stop building units and launch a final assault in a military game, or whether to call an opponent’s all-in in poker vs. folding and trying to find a better spot, or when to change gears from building power to going all-out for victory points in many Euro games.Read the rest of this post »

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Here is an idea for a bluffing game, one so simple that I could never market it in its basic form, and indeed would be surprised if I turned out to be the first to have come up with it. The basic idea is to guess how many chips your opponent is going to commit to the pot. He’d like to invest as little as possible, but if you guess correctly, you win, whereas if you’re wrong, now you must bet and he gets a guess.

The conclusions of my strategic analysis of a simple dice game, in a nutshell: 1) Don’t play it safe until your opponent has already failed or is likely to, 2) Either gamble a little more than your opponent, or play it much safer, 3) Don’t imitate your opponents in a multi-player game, and 4) Put your opponent on the most marginal decision possible.

Yesterday, I presented my analysis of the two-player version of a simple dice game I’d proposed. As you’d expect, it gets a lot more complicated when you add a third player; nonetheless, I do have some interesting results to present regarding perfect strategy for all three players.

An interesting exercise in probability: We have a die with an arbitrary number of sides, and players have to pick a target number to hit, with the winner being the one who picks the highest number while still managing to roll that number or higher. What does perfect play look like, how does it change with the die size, and how much of an advantage is it to pick second?

When the goal is a high score, a seemingly single-player game is actually more like an infinity-player game. Whereas most games ask us to be consistent about being good, high score games ask us to be good at being inconsistent.

Big group games have their own challenges on top of those of smaller multiplayer games. This is not a binary thing, however; we see these problems appear and grow gradually, as we increase the number of players. The main problems are: number of components, gang-up-on-the-leader phenomenon, long playtime, and long downtime between players’ turns.

As discussed previously, there are objective differences between games for two and games for groups. The biggest challenge for three- and four-player games is not so much how to balance the game, but how much to balance it, and how much that balance should depend on the factors of luck, individual skill, and player cooperation.

Two-player games are objectively very different from multiplayer games. For one thing, they are at least theoretically solvable, whereas “perfect play” is not always a real thing for multiplayer games. For another, there is no distinction between harming the opponent and helping oneself, as there is in a multiplayer game. Here, we discuss the unique challenges in designing a game for two.